Quantum spin liquid phase with spontaneous spin current in moiré transition metal dichalcogenides

At the filling of three electrons per unit cell in twisted bilayer transition metal dichalcogenides (TMDs) a lattice of Wigner molecules is formed. Leveraging the spin-orbital pseudospin degeneracy of the low-energy Hilbert space of each Wigner molecule, we demonstrate that TMD materials can host a general spin-orbital Hamiltonian on the triangular lattice that is tunable via the moiré superlattice spacing and dielectric environments. The quantum phase diagram for this model reveals a rich landscape of phases driven by spin-orbital interactions, ranging from ferri-electric valence bond solids to a quantum spin liquid. The quantum spin liquid, characterized by vanishing on site spin and pseudospin correlations, develops an order with finite spin current along the bonds of the lattice. Furthermore, the half system entanglement spectrum exhibits emergent spin momentum coupling in its low energy modes. Our work establishes moiré Wigner molecules lattices in TMD materials as a prominent platform for correlated spin-orbital phenomena.